Yes, the FIFA 23 Ultimate Team servers are currently down. Players are reporting problems connecting to the FUT Servers on March 3, 2023, at 4:30 PM GMT / 8:30 AM PT / 11:30 AM ET.
The servers were previously down today at 9:15 AM GMT / 1:15 AM PT / 4:15 AM ET for six hours but the issue has returned.
EA Sports announced on their support Twitter that they are aware of the problem and are currently investigating.
If you are still having issues, we recommend checking out the EAFIFADirect account on Twitter to gather more information.
This Twitter account will tweet out any planned outages or if there are issues with the servers. You can also check the FIFA 23 Trello Board, which may showcase any Ultimate Team server outage.
This may help you understand the connectivity issues you are facing. Another solution is to check if there are any current updates that need to be installed.

If there is no scheduled downtime, and you have checked all of the sources above, yet you still have issues, you may need to check the server status of your console.
There will also be a scheduled downtime whenever there is a new update to the game. The recent Title Update 6 had the game down for multiple hours.